With gas turbines, in particular ones having so-called silo combustion chambers, it is of interest to have an indicator for a disturbance to combustion processes at one or more of the burners. Instances of local overheating can, specifically, have negative effects on the service life of the gas turbine, for example. Since the direct measurement of the temperature distribution at the burners is difficult owing to the high combustion temperatures, the temperature measurement is carried out indirectly by measuring the exhaust gas temperature distribution. This is possible because the temperature distribution in the burner region is continued qualitatively via the gas flow as far as into the exhaust gas channel.